#2 & #3: Tweaking tone controls
On many Les Pauls and other 2HB guitars I wish that the neck pickup was a little brighter and the bridge pickup was a little darker. My solutions had usually involved replacing the tone pots or caps and/or magnets. Specifically to brighten up the neck pickup I might use a higher resistance pot and/or a smaller value tone capacitor, or replace an A2 magnet with A5. To cut the highs of a bridge pickup I might try the opposite.
I just figured out a much simpler method to brighten or darken a pickup. To brighten a neck pickup I can add a resistor in series with the 500K tone pot and .022uF tone cap to raise the net resistance. To make a bridge pickup less bright I can add a resistor between the two terminals used on the 500k tone pot (typically #1 and #2***) to lower the effective resistance.
In the first case (to make a pickup brighter) the math for adding a series resistor is simple: just add the two values. However to determine what value resistor to add in series is more complicated — you need to interrupt the signal path to insert the resistor. You can either wire in a pot temporarily and adjust it until you find the desired brightness, or wire in jumper clips to test different value resistors.
In the second case (to reduce the brightness of a pickup) the measurements are easier but the math is more complicated. With just two terminals used on a guitar tone pot you can determine the net resistance of your desired setting (like 8 out of 10) by subtracting the resistance between the unused terminal and the wiper (#2 and #3) from that between the outside terminals (#1 and #3). In the example below the desired net resistance of the tone control would be 400K (a 500K linear pot set to 8 of 10).¤¤¤
The math for adding a resistor in parallel with the active terminals on a 500k tone pot involves computing the reciprocal of the difference between the reciprocals of 500k and the added resistor across the #1 & #2 terminals on the tone pot.@@@
With just two terminals used on a typical treble cut tone control it is relatively simple to figure out the desired net resistance to cut the brightness of a pickup; if you want the bridge pu to be no brighter than the existing control set to, say, 8 (out of 10) first measure the resistance at that setting between the #1 & #3 terminals(A) and the #2 & #3 terminals(B). The math to determine the value resistor to add in parallel with the two terminals used (A & B) is more complicated — you must compute the reciprocal of the difference between the reciprocals of A and (A-B).
For example, with a 500k linear pot with a desired maximum value of 8 out of 10 we would compute:
1/(1/(A-B) - 1/A) = 1/(1/100K - 1/500K)
To simplify matters I always drop the K in the fractions and add it to the result:
1/(1/(500-100) - 1/500)
= 1(1/400 - 1/500)
= 1(.0025 - .002)
After adding the K suffix the answer is 2M
Which means that we would add a 2M resistor across the #1 & #2 terminals of a 500K tone pot to make the net resistance 400K so that it would get no brighter than the existing pot set to 8 out 10.
NOTE: By adding the resistor (called a tapering resistor) it would alter the taper of the pot a little bit. If I recall R.G.'s article correctly for a pot wired as a variable resistor it would make the taper more like a reverse audio pot. So turning down from 10 would go a little bit slower and turning up from 0 a little bit faster.
*** When I started writing articles on guitars and amps 20 years ago I did not know that there were any standards in numbering pot terminals so I usually referred to them as Wiper, CW & CCW or Wiper, Normally Hot & Normally Cold. However one of the standard numbering schemes is that the wiper is #2, the CCW terminal (typically connected to ground) is #1 and the CW terminal (not usually connected to ground) is #3.
Why? For one thing you can have a simple volume control with just the wiper connected to the hot signal and the CCW terminal connected to ground as I discovered in my 1939 Rickenbacher lap steel.
¤¤¤ In my example I used a 500K linear pot to simplify matters (a 500K pot set to 8 out of 10 will measure 100K between terminals #2 & #3.)
@@@ Alternately you could add a capacitor in parallel with the tone cap to increase the net capacitance to make the pickup darker, or in series to decrease the net capacitance to make it brighter. Of course we all know that the math for adding caps in parallel or series is the opposite of that for resistors.
P.S. Replacing controls on a Les Paul is a drag because they require a special more expen$ive pot with a longer bushing to go through the carved top. If at all possible I try to adapt the existing pots for my own nefarious schemes!